E. De Felice and F. De Laurentiis agree that the surname was normally formed from nicknames and trade names derived from sacco —as a container of hemp, jute or cloth—, referring to those who made and sold sacks, or to those who loaded, unloaded and transported sacks of goods.

Both note that, in some cases, it may be the aphaeretic hypocoristic of Isacco and its altered forms. De Felice specifies that this holds especially for Sacchi and Sacco, Sacchetti, Sacchini and Saccucci, and recalls that the great medieval Florentine family of the Sacchetti would go back to an Isacchetto, mentioned in Florence in the first years of the 11th century.

De Felice adds that the name Isacco, of tradition not only Jewish but also Protestant and Catholic, continues —through the Latin Isaac and the Greek Isaák— the biblical Hebrew name Yiṣḥaq ("God smiles" or "may God smile").

De Laurentiis agrees on the origin and the etymology, with the specification that the name means "God smiles" or "may God smile" at the birth of the expected and desired child. He notes that the surname Isacco is fairly common in Italy in the late Middle Ages and that the surname Sacchi is diffused throughout Italy.